Question

Question 1: Explain why it is a weakly dominant strategy for you to show up for both of your midterms, even if you have not studied at all. [Remember, I drop your worst midterm and replace it with the grade you receive on your final, provided this helps you.]

Answer 1

A weakly dominant strategy is a strategy that earns atleast as high a payoff as any other and earns strictly higher in atleast some situations.

It is a weakly dominant strategy to show up to both midterms even if you haven't studied at all,as your worst midterm will be replaced by the grade you receive on the final.

1) If you attend just 1 midterm and get 20%(Assuming you haven't studied), you get a 0 on the other midterm and that gets replaced by the grade you receive on the final(Let's say 30%)

2) However if you attend both the midterms, you will either score better in the 2nd midterm(let's say 25%) and your 1st midterm will be replaced by the final grade, so your score for 2 midterms will be 30% and 25%

In the worst case scenario where you do not score better than your 1st midterm,your 2nd midterm will be replaced by the final grade just as it would have been if you hadn't attended it at all.

So it is a weakly dominants strategy to show up to both midterms as it dominates the other strategy of attending just 1(or 0) in atleast some or all of the cases. You will score strictly higher if your 2nd midterm(One you would have skipped) ends up being better than 1st and end up equal if you don't.